Dagesh Qal (the Hebrew term), the “Weak Dagesh”, or Dagesh Lene (the Latin term, more common in grammars) is a dot that appears within one of the BGD KPRT consonants to indicate the harder (plosive) form of the double letter, in preference to the fricative (spirantized) form. The double letters are:

bet, gimel, dalet, kaf, peh, resh, tav.

Resh is only sometimes treated as a double letter, anciently in a few rare circumstances in Bible manuscripts, and in medieval mystical texts.

In modern Hebrew, only bet, kaf, and peh retain a distinction in pronunciation.

A Dagesh Lene will usually appear when one of the double letters begins a word, or when it begins a new syllable (usually after a closed syllable ending in a silent shewa)

The Dagesh Lene can also appear as the second of a two-consonant cluster of a closed syllable at the end of a word, when both it and the preceding consonant include a silent shewa. (Example: שָׁמַרְתְּ, sha-mar-t)

Vav does not take a dagesh, but a dot inside of it (which looks exactly like a dagesh) marks it as a matre lectionis. See: Shuruq.

The Dagesh Ḥazaq (Hebrew), “Strong Dagesh”, “Doubling Dagesh”, or Dagesh Forte (Latin, more commonly used in grammars) is used to indicate doubling (gemination) of a consonant, which also means that it form the ending of a closed syllable with the preceding consonant and vowel, in addition to acting as the beginning a new syllable.

Letters which can take a Dagesh Forte include any of the BGDKPRT letters, and most of the other letters as well: zeyin, tet, yod, lamed, mem, nun, samek, tsadi, qof, shin.

A Dagesh Forte can only exist in a medial position; it cannot begin or end a word.

Guttural letters cannot take a Dagesh Forte. They cannot be doubled. The letter resh has some exceptions to this, as it isn't fully treated as a guttural.

Any of the Matres Lectionis (alef, heh, vav, or yod) may have a dot inside of them (which looks identical to a dagesh). This is called a Mappiq, and means that the consonant should be fully pronounced.

For a vav, this is quite rare and may seem confusing as it will appear as what would normally be a shuruq, but the presence of a following vowel will be the clue that it is actually a mappiq.